Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj964 Structured version   Visualization version   Unicode version

Theorem bnj964 29826
 Description: Technical lemma for bnj69 29891. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj964.2
bnj964.3
bnj964.5
bnj964.8
bnj964.12
bnj964.13
bnj964.96
bnj964.165
Assertion
Ref Expression
bnj964
Distinct variable groups:   ,,,   ,   ,   ,,,   ,   ,,   ,,,   ,   ,
Allowed substitution hints:   (,,,,)   (,,,,,)   (,,,,,)   (,,)   (,,,,,)   (,,,,)   (,,)   (,,,,)   (,,,,)   (,,,,,)   (,,,,,)

Proof of Theorem bnj964
StepHypRef Expression
1 nfv 1769 . . . 4
2 bnj964.2 . . . . . . . 8
32bnj1095 29665 . . . . . . 7
4 bnj964.3 . . . . . . 7
53, 4bnj1096 29666 . . . . . 6
65nfi 1682 . . . . 5
7 nfv 1769 . . . . 5
8 nfv 1769 . . . . 5
96, 7, 8nf3an 2033 . . . 4
101, 9nfan 2031 . . 3
11 bnj255 29582 . . . . 5
12 bnj645 29632 . . . . . . 7
13 simp3 1032 . . . . . . . 8
1413bnj706 29636 . . . . . . 7
15 eleq2 2538 . . . . . . . . 9
1615biimpac 494 . . . . . . . 8
17 elsuci 5496 . . . . . . . . 9
18 eqcom 2478 . . . . . . . . . 10
1918orbi2i 528 . . . . . . . . 9
2017, 19sylib 201 . . . . . . . 8
2116, 20syl 17 . . . . . . 7
2212, 14, 21syl2anc 673 . . . . . 6
23 df-3an 1009 . . . . . . . . . . . . 13
24233anbi3i 1223 . . . . . . . . . . . 12
25 bnj255 29582 . . . . . . . . . . . 12
2624, 25bitr4i 260 . . . . . . . . . . 11
27 bnj345 29591 . . . . . . . . . . 11
28 bnj252 29580 . . . . . . . . . . 11
2926, 27, 283bitri 279 . . . . . . . . . 10
3011anbi2i 708 . . . . . . . . . 10
3129, 30bitr4i 260 . . . . . . . . 9
32 bnj964.96 . . . . . . . . 9
3331, 32sylbir 218 . . . . . . . 8
3433ex 441 . . . . . . 7
35 df-3an 1009 . . . . . . . . . . . . 13
36353anbi3i 1223 . . . . . . . . . . . 12
37 bnj255 29582 . . . . . . . . . . . 12
3836, 37bitr4i 260 . . . . . . . . . . 11
39 bnj345 29591 . . . . . . . . . . 11
40 bnj252 29580 . . . . . . . . . . 11
4138, 39, 403bitri 279 . . . . . . . . . 10
4211anbi2i 708 . . . . . . . . . 10
4341, 42bitr4i 260 . . . . . . . . 9
44 bnj964.165 . . . . . . . . 9
4543, 44sylbir 218 . . . . . . . 8
4645ex 441 . . . . . . 7
4734, 46jaoi 386 . . . . . 6
4822, 47mpcom 36 . . . . 5
4911, 48sylbir 218 . . . 4
50493expia 1233 . . 3
5110, 50alrimi 1975 . 2
52 bnj964.5 . . . . 5
53 vex 3034 . . . . 5
542, 52, 53bnj539 29774 . . . 4
55 bnj964.8 . . . 4
56 bnj964.12 . . . 4
57 bnj964.13 . . . 4
5854, 55, 56, 57bnj965 29825 . . 3
5958bnj115 29603 . 2
6051, 59sylibr 217 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wo 375   wa 376   w3a 1007  wal 1450   wceq 1452   wcel 1904  wral 2756  wsbc 3255   cun 3388  csn 3959  cop 3965  ciun 4269   csuc 5432   wfn 5584  cfv 5589  com 6711   w-bnj17 29563   c-bnj14 29565   w-bnj15 29569 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-8 1906  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639  ax-un 6602 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-iun 4271  df-br 4396  df-suc 5436  df-iota 5553  df-fv 5597  df-bnj17 29564 This theorem is referenced by:  bnj910  29831
 Copyright terms: Public domain W3C validator